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Deep Neural Network-Based Simulation of Sel’kov Model in Glycolysis: A Comprehensive Analysis

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  • Jamshaid Ul Rahman

    (School of Mathematical Sciences, Jiangsu University, 301 Xuefu Road, Zhenjiang 212013, China
    Abdus Salam School of Mathematical Sciences, GC University, Lahore 54600, Pakistan)

  • Sana Danish

    (Abdus Salam School of Mathematical Sciences, GC University, Lahore 54600, Pakistan)

  • Dianchen Lu

    (School of Mathematical Sciences, Jiangsu University, 301 Xuefu Road, Zhenjiang 212013, China)

Abstract

The Sel’kov model for glycolysis is a highly effective tool in capturing the complex feedback mechanisms that occur within a biochemical system. However, accurately predicting the behavior of this system is challenging due to its nonlinearity, stiffness, and parameter sensitivity. In this paper, we present a novel deep neural network-based method to simulate the Sel’kov glycolysis model of ADP and F6P, which overcomes the limitations of conventional numerical methods. Our comprehensive results demonstrate that the proposed approach outperforms traditional methods and offers greater reliability for nonlinear dynamics. By adopting this flexible and robust technique, researchers can gain deeper insights into the complex interactions that drive biochemical systems.

Suggested Citation

  • Jamshaid Ul Rahman & Sana Danish & Dianchen Lu, 2023. "Deep Neural Network-Based Simulation of Sel’kov Model in Glycolysis: A Comprehensive Analysis," Mathematics, MDPI, vol. 11(14), pages 1-9, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3216-:d:1199774
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    References listed on IDEAS

    as
    1. Stefan Kremsner & Alexander Steinicke & Michaela Szölgyenyi, 2020. "A Deep Neural Network Algorithm for Semilinear Elliptic PDEs with Applications in Insurance Mathematics," Risks, MDPI, vol. 8(4), pages 1-18, December.
    2. Logan G. Wright & Tatsuhiro Onodera & Martin M. Stein & Tianyu Wang & Darren T. Schachter & Zoey Hu & Peter L. McMahon, 2022. "Deep physical neural networks trained with backpropagation," Nature, Nature, vol. 601(7894), pages 549-555, January.
    3. Stefan Kremsner & Alexander Steinicke & Michaela Szolgyenyi, 2020. "A deep neural network algorithm for semilinear elliptic PDEs with applications in insurance mathematics," Papers 2010.15757, arXiv.org, revised Dec 2020.
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    Cited by:

    1. Jamshaid Ul Rahman & Sana Danish & Dianchen Lu, 2024. "Oscillator Simulation with Deep Neural Networks," Mathematics, MDPI, vol. 12(7), pages 1-15, March.
    2. Chih-Yu Liu & Cheng-Yu Ku & Wei-Da Chen, 2024. "A Spacetime RBF-Based DNNs for Solving Unsaturated Flow Problems," Mathematics, MDPI, vol. 12(18), pages 1-25, September.

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